Question

Pedro and João selected 15 balloons and numbered from 1 to 15. They created all the balloons and each one got the number of the balloon balloons burst. At the end of the game, João got double Pedro's points, despite having fewer balloons. So, as different possible ways that John uses his points are:

a. 2
b. 3
c. 4
d. 5

Answer 1

The question is a mathematical problem involving permutations and probabilities where João must double Pedro's points with fewer numbered balloons. By systematically finding combinations whose sums meet the criteria, we determine the ways João can achieve this.

Step-by-step explanation:

The student's question is a problem that involves counting and probabilities, which are topics in mathematics. Specifically, the problem is about finding the number of ways João can double Pedro's points by bursting fewer numbered balloons. We know that the balloons are numbered from 1 to 15, and the points are given according to the number on the balloon. Since João had fewer balloons but doubled Pedro's points, we need to find combinations of numbered balloons whose sum can be doubled by another combination that Pedro could have. To determine this, a systematic approach of pairing different combinations and calculating their sums is required.

Let's assume Pedro has a set of balloons which collectively are worth P points. João will then need balloons worth 2P points. By trying different combinations, the correct answer can be found, which refers to the number of ways João can achieve his double points despite having fewer balloons.